May a common carrier be held liable to a passenger who was injured and eventually died while trying to board the vehicle?

Yes. It is the duty of common carriers of passengers to afford passengers an opportunity to board and enter, and they are liable for injuries suffered by boarding passengers resulting from the sudden starting up or jerking of their conveyances while they are doing so. The victim, by stepping and standing on the platform of the bus, is already considered a passenger and is entitled all the rights and protection pertaining to such a contractual relation. (Dangwa Transportation Co., Inc. v. CA, G.R. No. 95582, Oct. 7, 1991)